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S 3yo Example 2 Testing a Claim about the Population Mcan (Left-tailed Test) wre

ID: 3044714 • Letter: S

Question

S 3yo Example 2 Testing a Claim about the Population Mcan (Left-tailed Test) wre speeds (in mi/h) measured from southbound traffic on I-280 near Cupertino, alifornia (based on data from Sig'Alert). This simple random sample was obtained at 3:30 p.M on a weekda with a mean that is less than the speed limit of 65 mi/h. Solution Step 1 Determine the Null (Ho) and Alternative (Hi) Hypotheses Use a 005 significance level to test the claim that the sample is from a population Step 2 Determine the Level of Significance a oc 2005" Determine the Type of Test Step 3 et Determine the Test Statistic to Lo Step 4 S. Step 5 Determine the Critical Value ta Step 6 Conclusion

Explanation / Answer

Solution:-

Step - I

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: > 65
Alternative hypothesis: < 65

Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small.

Step - II

Formulate an analysis plan. For this analysis, the significance level is 0.05.

Step- III

The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = s / sqrt(n)

DF = n - 1

Step - IV

t = (x - ) / SE

Step - V

talpha/2 = This value can be found by uisng alpha/2 and degree of freedom in t-calculator.

where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.

Step - VI

Interpret results.

Case - I If the P-value is greater than the significance level (0.05), we cannot reject the null hypothesis.

CaseII - If the P-value is less than the significance level (0.05), we have to reject the null hypothesis.